**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Publication# Iterative pre-conditioning for expediting the distributed gradient-descent method: The case of linear least-squares problem

Abstract

This paper considers the multi-agent linear least-squares problem in a server-agent network architecture. The system comprises multiple agents, each with a set of local data points. The agents are connected to a server, and there is no inter-agent communication. The agents' goal is to compute a linear model that optimally fits the collective data. The agents, however, cannot share their data points. In principle, the agents can solve this problem by collaborating with the server using the server-agent network variant of the classical gradient-descent method. However, when the data points are ill-conditioned, the gradient-descent method requires a large number of iterations to converge. We propose an iterative pre-conditioning technique to mitigate the deleterious impact of the data points' conditioning on the convergence rate of the gradient-descent method. Unlike the conventional preconditioning techniques, the pre-conditioner matrix used in our proposed technique evolves iteratively. We show that our proposed algorithm converges linearly with an improved rate of convergence in comparison to both the classical and the accelerated gradient-descent methods. For the special case, when the solution of the least-squares problem is unique, our algorithm converges to the solution superlinearly. Through numerical experiments on benchmark least-squares problems, we validate our theoretical findings, and also demonstrate our algorithm's improved robustness against process noise. (C) 2021 Elsevier Ltd. All rights reserved.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (7)

Related publications (3)

Algorithm

In mathematics and computer science, an algorithm (ˈælɡərɪðəm) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually.

Gradient descent

In mathematics, gradient descent (also often called steepest descent) is a iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a local maximum of that function; the procedure is then known as gradient ascent.

Dijkstra's algorithm

Dijkstra's algorithm (ˈdaɪkstrəz ) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, road networks. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. The algorithm exists in many variants. Dijkstra's original algorithm found the shortest path between two given nodes, but a more common variant fixes a single node as the "source" node and finds shortest paths from the source to all other nodes in the graph, producing a shortest-path tree.

Nicolas Henri Bernard Flammarion, Aditya Vardhan Varre

We consider stochastic approximation for the least squares regression problem in the non-strongly convex setting. We present the first practical algorithm that achieves the optimal prediction error ra

2022This article considers solving an overdetermined system of linear equations in peer-to-peer multiagent networks. The network is assumed to be synchronous and strongly connected. Each agent has a set o

Finding convergence rates for numerical optimization algorithms is an important task, because it gives a justification to their use in solving practical problems, while also providing a way to compare

2017